Step 1:

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The conic equation is $\"image\"$

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The coefficients of $\"image\"$ and $\"image\"$ are the same sign but unequal coefficients. So the equation is ellipse.

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Convert the equation in standard form of ellipse.

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$\"image\"$

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$\"image\"$

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$\"image\"$

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$\"image\"$

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Compare it to standard form of horizontal ellipse $\"image\"$ .

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Where $\"image\"$

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$\"image\"$ is length of semi major axis and $\"image\"$ is length of semi minor axis.

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Center is $\"\"$ , vertices $\"image\"$

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Foci $\"image\"$ and $\"image\"$ .

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In this case $\"image\"$ .

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Center is $\"image\"$ .

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Vertices $\"image\"$

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Foci $\"image\"$ .

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Eccentricity $\"image\"$

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$\"image\"$ .

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Step 2:

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Graph:

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Draw the coordinate plane.

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Plot the center, vertices and foci of ellipse.

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Then sketch the ellipse by using the semi major axis length is 2.82 units and semi minor axis length is 1.414 units.

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$\"\"$

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Solution:

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Center $\"image\"$ , vertices $\"image\"$ .

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Foci $\"image\"$ and $\"image\"$ .